MT004 MIDTERM 3 SAMPLE 1
İLKER S. YÜCE
DECEMBER 5, 2009
QUESTION 1. VISUAL REPRESENTATION OF DATA
2008 U.S. Defense Employees
Branch Officers and Enlistees
Army 525,482
Navy 331,383
Marine Corps. 190,651
Air Force 327,589
Display the data from the table in a Bar Chart.
QUESTION 2. FREQUENCY AND PROBABILITY DISTRIBUTIONS
Define random variables Xand Yaccording to the following tables:
k P(X=k)
1 .1
3 .2
5 .3
8 .4
k P(Y=k)
-1 .1
3 .2
6 .3
10 .4
Assume that Xand Yare independent variables, i.e., P(X=n AND Y =m) = P(X=n)×P(Y=m).
(a) Write down the event X6=Yas a set of outcomes and calculate P(X6=Y).
(b) Write down the event X=Yas a set of outcomes and calculate P(X=Y).
QUESTION 3. BINOMIAL TRIALS
Suppose that a lot of 300 electrical fuses contains 5% defective. If a sample of five fuses is tested, find the
probability of observing at least one defective. (Remark. Since the lot is large, it is reasonable to assume
that the random variable Y, the number of defective observed, is approximately binomial distribution.)
QUESTION 4. THE MEAN
Student Areceived the following course grades during her first year of college: 4,4,4,4,3,3,2,2,2,0.
Student Breceived the following course grades during her first year of college: 4,4,4,4,4,4,3,1,1,1.
(a) Compute the population mean for each student.
(b) Which student had the better grade point average?
QUESTION 5. THE VARIANCE AND STANDARD DEVIATION
For the probability distribution in the given table below for a random variable Y, find its mean, variance,
and standard deviation.
y P(y)
0 1/8
1 1/4
2 3/8
3 1/4
QUESTION 6. CHEBYCHEV’S INEQUALITY
The number of customers per day at a certain sales counter denoted by Y, has been observed for a long
period of time and found to have a mean(µ) of 20 customers with a standard deviation(σ) of 2 customers.
The probability distribution of Yis not known. What can be said about the probability that Ywill be
between 16 and 24 tomorrow?
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